For any pure state \(|\psi \rangle =\sum _{i=0}^{d-1} \psi _i |i\rangle \) ,
the vector \(\left(r_0, r_1, \ldots , r_{d-1}\right)^\)  with
\(r_i:=\left|{1mu}\psi _i {1mu}\right|^2\)  is called the coherence vector of a
pure state \(|\psi \rangle \)  [1]}, [2]}. Based on the variance
\(\operatorname{Var}(|\psi \rangle , A)&=&\left\langle \psi  \left| A^2 \right| \psi  \right\rangle  -\left\langle \psi  \left| A \right| \psi  \right\rangle ^2,\) 
